SOLUTION: Give both an exact solution and an approximate solution to two decimal places for the following. Given: right △ABC with m∠C = 90° and m∠BAC = 60° point D on BC AD bise

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Question 1193626: Give both an exact solution and an approximate solution to two decimal places for the following.
Given:
right △ABC with m∠C = 90° and m∠BAC = 60°
point D on BC
AD bisects ∠BAC and AC = 3radical 3
Find: BD
exact BD =

approximate BD =

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Draw this.
ADC is a 30-60-90 right triangle, so AD is the hypotenuse. If the long leg (adj to angle 60) is sqrt(3), then the length of CD is 3, AC divided by sqrt (3). That makes AD, the hypotenuse, 6.
For BD, look at the whole 30-60-90 triangle BAC. If AC is 3 sqrt(3) then the hypotenuse AB is 6 sqrt(3). Therefore BC has to be 3 sqrt(3)*sqrt(3)=9, and BD must be 6.